The pattern everyone quotes
Gold is said to be strong in January and September, weak in the summer. These claims are repeated every year, usually with a chart of average monthly returns and no error bars.
Average monthly returns will always show a pattern. Even if the underlying process is pure noise, one month has to come out on top. The question is never "is there a pattern?" — it is "is the pattern bigger than what random data would produce?"
The test
This is a permutation test, and it is the correct tool:
- Compute the observed statistic — say, the spread between the best and worst month's average return.
- Shuffle the returns randomly, breaking any link to the calendar.
- Recompute the same statistic on the shuffled data.
- Repeat a few thousand times.
- Compare your observed value to that distribution.
If your observed spread sits comfortably inside the shuffled distribution, the seasonality is indistinguishable from noise. Not "probably noise" — statistically, you cannot tell the difference.
Why this matters beyond seasonality
The same procedure applies to every pattern you have ever found. A moving-average crossover that "works on gold." A day-of-week effect. A setup that fires after a certain candle. All of them should be tested against shuffled data before you risk money on them, because the human pattern-matching instinct is extremely good at finding structure in randomness and extremely bad at knowing how much structure randomness produces.
The multiple-comparisons problem
Even with a correct test, you have to be honest about how many patterns you examined before finding this one. If you tested twenty seasonal ideas and one came back significant at the 5% level, that is exactly what you would expect from chance. Adjust your expectations, or test on data you did not use to find the idea.
How to check this yourself
Sketch a monthly seasonality table for gold from ten years of returns, then ask the only question that matters: is the gap between the best and worst month bigger than what you would get by shuffling the same returns at random? Almost always it is not. If you cannot separate the pattern from noise, you cannot trade it.